Diffusion and long-time tails in the overlapping Lorentz gas

A number of new features of the overlapping Lorentz gas are obtained using a method based on describing the system as a random walk on a disordered lattice. The velocity correlation function is shown to have a contribution which decays like $t^{\mathrm{-}[2+1/(d\mathrm{-}1\left)\right]}$. This term is the dominant long-time tail for d>3 and above the percolation threshold. New values are obtained for the exponents describing the vanishing of the diffusion coefficient and the intermediate-time tail near threshold.